The Forced vibration analysis of sandwich plates with an auxetic honeycomb core and laminated composite three-phase skin layers resting on Kerr foundation

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Abstract

This paper introduces isogeometric analysis (IGA) based on higher-order shear deformation theory (HSDT) for vibration analysis of sandwich plates resting on Kerr foundation (KF). The sandwich plates include the ultra-light of an auxetic honeycomb core layer and are reinforced by two laminated composite three-phase skin layers. The governing equation is derived from Hamilton's principle. The Newmark-β method is applied to solve the forced vibration of the sandwich plates by the code in Matlab software. The accuracy of the proposed method is verified through comparative examples. Additionally, the effects of geometrical dimensions, material properties, and foundation stiffness on the forced vibration of sandwich plates are studied in detail.

References

[1]. Wan, H., Ohtaki, H., Kotosaka, S., & Hu, G. “A study of negative Poisson's ratios in auxetic honeycombs based on a large deflection model”. European Journal of Mechanics-A/Solids, 23(1), 95-106, (2004). DOI: https://doi.org/10.1016/j.euromechsol.2003.10.006

[2]. Zhang, X.-C., An, L.-Q., Ding, H.-M., Zhu, X.-Y., & El-Rich, M. “The influence of cell micro-structure on the in-plane dynamic crushing of honeycombs with negative Poisson’s ratio”. Journal of Sandwich Structures & Materials, 17(1), 26-55, (2015). DOI: https://doi.org/10.1177/1099636214554180

[3]. Zhu, X., Zhang, J., Zhang, W., & Chen, J. “Vibration frequencies and energies of an auxetic honeycomb sandwich plate”. Mechanics of Advanced Materials and Structures, 26(23), 1951-1957, (2019).

[4]. Cong, P. H., Khanh, N. D., Khoa, N. D., & Duc, N. D. “New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT”. Composite Structures, 185, 455-465, (2018). DOI: https://doi.org/10.1016/j.compstruct.2017.11.047

[5]. Nguyen, D. D., & Pham, C. H. “Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson’s ratio in auxetic honeycombs”. Journal of Sandwich Structures & Materials, 20(6), 692-717, (2018). DOI: https://doi.org/10.1177/1099636216674729

[6]. Pham, Q.-H., Nguyen, P.-C., Tran, T. T., & Nguyen-Thoi, T. “Free vibration analysis of nanoplates with auxetic honeycomb core using a new third-order finite element method and nonlocal elasticity theory”. Engineering with Computers, 1-19, (2023). https://doi.org/10.1007/s00366-021-01531-3

[7]. Cheng, Y., Zhang, K., Liang, B., Cheng, H., Hou, G., Xu, G., & Jin, W. “Micromechanics of CNT grafted FRP based on hierarchical homogenization of transversely isotropic multi-coated model”. International Journal of Mechanical Sciences, 161, 105014, (2019). DOI: https://doi.org/10.1016/j.ijmecsci.2019.105014

[8]. Swain, A., & Roy, T. “Viscoelastic modelling and dynamic characteristics of CNTs-CFRP-2DWF composite shell structures”. Composites Part B: Engineering, 141, 100-122, (2018).

[9]. Seidi, J., & Kamarian, S. “Free vibrations of non-uniform CNT/fiber/polymer nanocomposite beams”. Curved and Layered Structures, 4(1), 21-30, (2017). DOI: https://doi.org/10.1515/cls-2017-0003

[10]. Yousefi, Amir Hossein, et al. "Dynamic characteristics of truncated conical panels made of FRPs reinforced with agglomerated CNTs." Structures. Vol. 33. Elsevier, (2021). DOI: https://doi.org/10.1016/j.istruc.2021.07.046

[11]. Noroozi, Mohammad, Zajkani, Asghar, & Ghadiri, Majid. “Dynamic plastic impact behavior of CNTs/fiber/polymer multiscale laminated composite doubly curved shells”. International Journal of Mechanical Sciences, 195, 106223, (2021). DOI: https://doi.org/10.1016/j.ijmecsci.2020.106223

[12]. Hughes, Thomas JR, Cottrell, John A, & Bazilevs, Yuri. “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement”. Computer methods in applied mechanics and engineering, 194 (39-41), 4135-4195, (2005). DOI: https://doi.org/10.1016/j.cma.2004.10.008

[13]. Affdl, JC Halpin, & Kardos, JL. “The Halpin‐Tsai equations: a review”. Polymer Engineering & Science, 16 (5), 344-352, (1976). DOI: https://doi.org/10.1002/pen.760160512

[14]. Nasution, Mahyuddin KM, Syah, Rahmad, Ramdan, Dadan, Afshari, Hassan, Amirabadi, Hossein, Selim, Mahmoud M,… Su, Chia-Hung. “Modeling and computational simulation for supersonic flutter prediction of polymer/GNP/fiber laminated composite joined conical-conical shells”. Arabian Journal of Chemistry, 15 (1), 103460, (2022). DOI: https://doi.org/10.1016/j.arabjc.2021.103460

[15]. Keshtegar, Behrooz, Motezaker, Mohsen, Kolahchi, Reza, & Trung, Nguyen-Thoi. “Wave propagation and vibration responses in porous smart nanocomposite sandwich beam resting on Kerr foundation considering structural damping”. Thin-Walled Structures, 154, 106820, (2020). DOI: https://doi.org/10.1016/j.tws.2020.106820

[16]. Reddy, Junuthula Narasimha. “Mechanics of laminated composite plates and shells: theory and analysis”: CRC press, (2003). DOI: https://doi.org/10.1201/b12409

[17]. Wolf J. “Dynamic SoilStructure Interaction”. PrenticeHall. Inc., Englewood Cliffs, New Jersey. (1985).

[18]. Abuteir, BW, Harkati, E, Boutagouga, D, Mamouri, S, & Djeghaba, K. “Thermo-mechanical nonlinear transient dynamic and Dynamic-Buckling analysis of functionally graded material shell structures using an implicit conservative/decaying time integration scheme”. Mechanics of Advanced Materials and Structures, 29(27), 5773-5792, (2022). DOI: https://doi.org/10.1080/15376494.2021.1964115

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Published

26-05-2025

How to Cite

[1]
T. S. Le, “The Forced vibration analysis of sandwich plates with an auxetic honeycomb core and laminated composite three-phase skin layers resting on Kerr foundation”, JMST, vol. 103, no. 103, pp. 110–120, May 2025.

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Mechanics & Mechanical engineering